Question

((Picture) CONVERGENT AND DIVERGENT SERIES PLEASE HELP!!

Answer 1

Answer:

This series is convergent

(A)

Step-by-step explanation:

We are given a series

Firstly, we will find nth term

So, numerator is

$=2n+1$

So, denominator is

$=n!$

so, nth term will be

$a_n=\frac{2n+1}{n!}$

now, we can use ratio test

$L= \lim_{n \to \infty} \frac{a_n_+_1}{a_n}$

$L= \lim_{n \to \infty} \frac{\frac{2n+3}{(n+1)!}}{\frac{2n+1}{n!}}$

$L= \lim_{n \to \infty} \frac{2n+3}{\left(n+1\right)\left(2n+1\right)}$

Since, denominator has two n terms

so, we get

$L=0$

So, this series is convergent